Abstract
It is shown that, modulo the automorphisms which fix the canonical diagonal MASA point-wise, the group of those automorphisms of O_n which globally preserve both the diagonal and the core UHF-subalgebra is isomorphic, via restriction, with the group of those homeomorphisms of the full one-sided n-shift space which eventually commute along with their inverses with the shift transformation. The image of this group in the outer automorphism group of O_n can be embedded into the quotient of the automorphism group of the full two-sided n-shift by its center, generated by the shift. If n is prime then this embedding is an isomorphism.
Original language | English |
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Journal | Journal für die reine und angewandte Mathematik |
Volume | 2012 |
Issue number | 667 |
Pages (from-to) | 177-191 |
ISSN | 0075-4102 |
DOIs | |
Publication status | Published - 2012 |
Keywords
- Cuntz algebra
- automorphism
- MASA
- shift automorphism
- UHF-subalgebra
- shift endomorphism